Question

The distance of a point $\mathrm{P}\left(\mathrm{a},\mathrm{b},\mathrm{c}\right)$ from the x-axis is

• A. $\sqrt{{\mathrm{a}}^2+{\mathrm{b}}^2}$
• B. $\sqrt{{\mathrm{b}}^2+{\mathrm{c}}^2}$
• C. $\mathrm{a}$
• D. $\sqrt{{\mathrm{a}}^2+{\mathrm{c}}^2}$

Answer 1

The correct option is B

$\sqrt{{\mathrm{b}}^2+{\mathrm{c}}^2}$

Explanation for the correct option:

Finding the distance from the axis:

Illustrating the diagram using the given information.

The distance of P from x-axis can be calculated by calculating the distance between P and its perpendicular drop which is $\mathrm{E}\left(\mathrm{a},0,0\right)$, as given in the above image.

Hence,

$\begin{array}{rcl}\text{Distance}& =& \sqrt{({\mathrm{x}}_2-{\mathrm{x}}_1{)}^2+({\mathrm{y}}_2-y_1{)}^2+({\mathrm{z}}_2-z_1{)}^2}\\ & =& \sqrt{(\mathrm{a}-\mathrm{a}{)}^2+(\mathrm{b}-0{)}^2+(\mathrm{c}-0{)}^2}\end{array}$

$=\sqrt{{\mathrm{b}}^2+{\mathrm{c}}^2}$

Therefore, the distance of a point $\mathrm{P}\left(\mathrm{a},\mathrm{b},\mathrm{c}\right)$ from the x-axis is $\sqrt{{\mathrm{b}}^2+{\mathrm{c}}^2}$

Hence, option (B) is the correct answer.